 # Weighted Average Formula

Weighted average is one of the most commonly employed measures in statistical data to find the average of quantities when each quantity has a certain weight. Let’s have a look at the definition and formula of weighted average here.

## What is the weighted average?

Weighted average is an average in which each quantity to be averaged is assigned a weight. These weightings determine the relative importance of each quantity on average. Weightings are the equivalent of having that many like items with the same value involved in the average.

## Formula for Weighted average

Let xi be the observations and wi be the weights of the observations; the formula of the weighted average is given below.

$$\begin{array}{l}\large \overline{x}\ or\ W=\frac{w_1x_1 + w_2x_2 + w_3x_3 + … + w_nx_n}{w_1 + w_2 + w_3+…w_n}\end{array}$$

This can also be written as:

$\large \overline{x}=\frac{\sum_{i=1}^{n}w_{i}x_{i}}{\sum_{i=1}^{n}w_{i}}$

Here,

x̄ or W = Weighted average

n = Number of terms to be averaged

wi = Weights applied to x values

xi = Data values to be averaged

In simple terms, we can write the above formula as:

$\large Weighted\;Average=\frac{Sum\;of\;Weighted\;Terms}{Total\;Number\;of\;Terms}$

To find the weighted term, multiply each term by its weighting factor, which is the number of times each term occurs.

Also, try: Weighted Mean Calculator

### Solved Example

Example 1: A class of 25 students took a science test. 10 students had an average score of 80. The other students had an average score of 60. What is the average score of the whole class?

Solution:

Step 1: To get the sum of weighted terms, multiply each average by the number of students that had that average and then add them up.

80 × 10 + 60 × 15 = 800 + 900 = 1700

i.e. Sum of weighted terms = 1700

Step 2: Total number of terms = Total number of students = 25

Step 3: Using the formula,

$$\begin{array}{l}\large Weighted\;Average=\frac{Sum\;of\;Weighted\;Terms}{Total\;Number\;of\;Terms}\end{array}$$

= 1700/25

= 68

Answer: The average score of the whole class is 68.

Example 2:

Calculate the weighted average for the following data:

 Data values 4 7 5 9 Weights 1 2 3 2

Solution:

From the given,

 Data values (xi) 4 7 5 9 Weights (wi) 1 2 3 2 wixi 4 14 15 18

∑wixi = 4 + 14 + 15 + 18 = 51

∑wi = 1 + 2 + 3 + 2 = 8

Weighted average = (∑wixi)/∑wi

= 51/8

= 6.375

Therefore, the weighted average of the given data is 6.375.